Stats Exam questions

Markus is testing the claim that the proportion of people who like olives is not equal to 50%. He rejects the null hypothesis at the a = 0.05 level. Which of the following options could be the corresponding 95% confidence interval for the same sample?

(0.07, 0.09)

Mike is studying the runtime of three sorting algorithms for lists of numbers on a newly-designed CPU. He knows that 40% of the time, mergesort runs the fastest, and that 30% of the time, quicksort is the fastest. The rest of the time, intertionsort is the fastest. Mike sorts 160 randomly selected lists on the new CPU. What is the expected value of the number of times that quicksort is the fastest?

48

Which of the following is NOT a sampling scheme?

Block

Which of the following would result in a narrower confidence interval?

Choosing a smaller confidence level

The companies (A) and (B) report teh average monthly sales for their employees as normally distrbuted with means of $50,000 and $55,000, respectively, and standard deviations of $3,000 and $6,000, respectively. Two employees (a) and (b) from each company have monthly sales of $54,000 and $60,000, respectively. Which employee is performing the best relative to the average performance in their own company?

Employee (a)

If the p-value is larger than the significance level, we

Fail to reject the null hypothesis, because it is likely that the observed difference occurs by random chance under the null hypothesis.

Which of the following statements is FALSE regarding simple linear regression?

Failure to reject the hypothesis 𝐻0: 𝛽1 = 0 indicates that variables X and Y have a significant association at the given significance level.

The researchers are interested in testing whether the proportion of college students attending football games this year has increased from 2008. Let p1 be the proportion who attended in 2008 and p2 be the proportion who attended this year. What should their null and alternative hypotheses be?

H0: p1-p2 = 0, HA: p1-p2<0

CJ is a disc golf player, and he is working on his drive (throwing it as far as possible) before his next tournament. Throughout the week, he averages a driving distance of 380.4 feet. The average disc golf drive for all disc golf players is 300 feet. If CJ wants to test if his average drive is significantly better than the average drive of all disc golf players, what hypotheses should he use?

H0: u=300, HA: u>300

A two-sample t-test for the difference in population means is conducted. Which is NOT a possible alternative hypothesis?

HA∶ 𝜇1 = 𝜇2

A company claims that the average lifetime of their light bulbs is 1000 hours. Nicho, who is a statistician at the company, wants to test if the actual average is greater than 1000 hours. What type of inference is most appropriate for Nicho to use?

Hypothesis test for a mean

. When comparing the average first 10 meter split and the average last 10 meter split of runners' 100 meter dash times, which of the following statistical inference methods would provide a probability for observing a more extreme difference if our initial assumption is there is no difference?

Hypothesis test for the mean difference

Which of the following is true about the correlation coefficient, r, in linear regression?

If the correlation coefficient is negative, the slope of the regression line will also be negative.

Which one is CORRECT about confidence intervals?

In repeated sampling, the process used to calculate the interval has a 95% probability of containing the population mean difference.

Which of the following best describes why the choice of significance level is important in interpreting a hypothesis test's results?

It fixes the Type I error rate of the hypothesis test under repeated sampling.

The Stanford Prison Experiment was a well-known psychological experiment in which 24 college students were given two different roles: guards and prisoners. The psychologists running the experiments examined the subjects' response to their role assignment. To minimize lurking variables, psychological tests were given to each participant and the experimenters matched each participant to the participant that performed the most similarly on the tests. Within each pairing, a fair coin was flipped to determine which participant would be a guard and which would be a prisoner. Which randomization method was utilized in this experiment?

Matched Pairs Design

boxplot, which measure of center would be most appropriate to summarize this data?

Median

A random sample of NC State students was taken and a 95% confidence interval for the average height (in feet) is obtained to be (5.4, 6.1). Here are two interpretations: I. There is a 95% chance that the true average height of students at NC State is between 5.4 feet and 6.1 feet. II. If we obtained 100 random samples and computed a 95% confidence interval for the mean each time, we would expect that exactly 95 of them would have the true mean between 5.4 feet and 6.1 feet. Determine which, if any, of the interpretations are correct.

Neither Interpretation is correct

Let X represent the scores on a university entrance exam, adjusted such that the scores follow a Normal distribution with mean of 0 and standard deviation of 2. Which of the following probabilities are approximately equal under this distribution?

P(-2<X<2), P(-1<Z<1) where Z-N(0,1) and Probability between the 16th and 84th percentiles

. In hypothesis testing, if the p-value is less than the chosen significance level (α), what is the correct statistical decision?

Reject the null hypothesis

We are able to perform statistical inference because

Sample statistics have predictable distributions

A large nationwide poll recently showed an unemployment rate of 9% in the US. The mayor of a local town wonders if this national result holds true for her town, so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9% in her town. Let p represent the unemployment rate in her town. Here are the hypotheses she'll use: � = 0.09 � ≠ 0.09 Under which of the following conditions would the mayor commit a Type I error?

She concludes the town's unemployment rate is not 9% when it actually is.

Mei is creating a confidence interval for the mean number of students in her district affected by the flu each year. Mei originally had n = 32 data points, but she recently acquired data for the most recent year, bringing her total up to n = 33 data points. What will happen to her critical value and degrees of freedom with the added data point?

She'll go from a t-distribution with 31 to 32 degrees of freedom, so the critical value will get smaller.

A company tracks the number of products sold across four different regions in a quarter. To compare the sales figures for each region, which of the following types of graphs would be most appropriate?

Simple bar chart

Approximately 93% of Americans eat ice cream. Suppose a random sample of 3 Americans is taken; which of the following best describes the sampling distribution of the sample proportion of Americans who eat ice cream?

Skewed left: The sample size is small, so the sampling distribution is skewed similarly to the population distribution.

Barry and Tasha are researching whether people living with cats are happier than people living with dogs. They found subject who lived with cats only for the last year and separately found subjects who lived with dogs only. They then recorded data concerning their happiness. Barry argues that this is an experiment, but Tasha disagrees with him-She thinks that this is an observational study. Who is right, and why?

Tasha is right. They do not assign cats of dogs to these people, so this is an observational study.

interquartile

Tells you the spread of the middle half of your distribution

In a clinical trial, a pharmaceutical company tests a new drug on 400 random selected patients with a specific condition. The average recovery time for the patients taking the drug is found to be 5.7 days. Based on the reported statistic, what parameter the company is interested in?

The average recovery time of all patients with the condition who take the new drug.

Which of the following is true about the correlation coefficient r?

The correlation coefficient is always between -1 and +1

Given the histogram below for a set of data, which statement is true?

The median would be a better measure of the center of the data than the mean.

z-score tells you

The number of standard deviations that x is away from the mean

Which of the following best defines the p-value:

The probability of observing a test statistic as extreme or more extreme than that which was observed, if the null hypothesis is true.

. For a given 99% confidence interval of (1.5, 2.8), we know that:

The probability that this confidence interval contains the true parameter is either 100% or 0%.

Cluster Sampling

The sampling method in which the population is first divided into non-overlapping groups and a simple random sample of those groups is selected with all individuals in the selected groups being included in the sample.

Which of the following is NOT true about the margin of error (MOE) when estimating the population proportion?

The value of the sample proportion is not related to the width of the confidence interval.

A sports reporter is interested in finding out which college football team has the most support within their state of North Carolina. They randomly interview 200 people in their city and conclude that Duke is the most popular football team in the state. What type of sampling bias has likely occured?

Undercoverage

Which of the following is NOT an example of statistical inference?

Use mathematics to relate population parameters to sample statistics.

A health survey was conducted to estimate the proportion of adults in a city who have a BMI classified as "obese" (BMI ≥ 30). A random sample of 400 adults was selected, and the 95% confidence interval for the proportion of adults classified as obese is (0.19, 0.31). Which of the following statements is correct?

We are 95% confident that the proportion of obese adults in the city is between 19% and 31%.

Wildlife researches were studying the weighs of Amur Leopards, a nearly extinct subspecies of leopard native to Southeast Russia. After collecting a sample of size 20, the researches found a mean weight of 82.1 pounds with standard deviation 13.3 pounds.

We do not have enough information to determine the mean or standard deviation of the sampling distribution.

If a hypothesis is not rejected at the 0.10 level of significance, it

Will not be rejected at the 0.05 level of significance.

A statistic

a numerical value calculated from a sample of data. Examples include sample mean, sample standard deviation

A parameter

a numerical value that describes a population. Examples include population mean, population standard deviation

Which measure of center is most affected by outliners?

mean

Both Linear Data and Constant Variance is violated

not a straight line, and the spread of data points around that line is not consistent across the range of the independent variable

What is a requirement for an Experimental Design?

randomization

median

the middle score in a distribution; half the scores are above it and half are below it

Block Design

the random assignment of units to treatments is carried out separately within each block

Completely randomized

type of experiment in which all experimental units have an equal chance of receiving any treatment

An instructor of ST311 is interested in the distribution of the scores on the first midterm exam. To select a sample from the population, the instructor came up with the following two methods:

A= Stratified random sampling, B= Cluster sampling

mean

average